Slope Showdown: Real-Life Comparisons for Grade 7

1. Sarah and Tom are walking up two different hills. Sarah's hill rises from (2, 3) to (5, 9), while Tom's hill rises from (1, 2) to (4, 8). Calculate the slope of each hill and determine who has a steeper hill.

• Tom's hill has a slope of 1, making it less steep.

• Sarah's hill is steeper by a slope of 2.5.

• Sarah's hill has a slope of 3, making it steeper.

• Both hills have the same slope of 2, so neither is steeper.

2. A car travels from point A (0, 0) to point B (4, 8) and another car travels from point C (1, 1) to point D (5, 5). Find the slope of each car's path and interpret which car is going uphill more steeply.

• Car A to B has a slope of 0.5, which is steeper than car C to D with a slope of 1.2.

• Car A to B has a slope of 1, which is steeper than car C to D with a slope of 2.

• Car A to B has a slope of 3, which is steeper than car C to D with a slope of 1.5.

• Car A to B has a slope of 2, which is steeper than car C to D with a slope of 1.

3. In a park, a slide rises from (0, 0) to (6, 4) and a swing set rises from (1, 2) to (5, 6). Calculate the slopes of both the slide and the swing set. Which one is steeper and what does that mean for the kids using them?

• The slide is steeper than the swing set.

• The slide is less steep than the swing set.

• Both the slide and swing set have the same slope.

• The swing set is steeper than the slide.

4. A bike path goes from (3, 2) to (7, 10) while a walking path goes from (2, 1) to (6, 5). Determine the slope of each path and explain which path is steeper and how that might affect bikers and walkers.

• The bike path has a slope of 3, and the walking path has a slope of 0.5. The bike path is less steep.

• The bike path has a slope of 2, and the walking path has a slope of 1. The bike path is steeper.

• Both paths have a slope of 2, making them equally steep.

• The bike path has a slope of 1, and the walking path has a slope of 2. The walking path is steeper.

5. A train travels from station A at (0, 0) to station B at (10, 20) and another train travels from station C at (2, 4) to station D at (8, 16). Calculate the slopes and discuss which train is traveling at a steeper incline.

• Train C travels at a steeper incline than Train A.

• Both trains travel at the same incline.

• Train A has a steeper incline than Train C.

• Train B travels at a shallower incline than Train D.

6. A ramp for skateboarding rises from (0, 0) to (5, 5) and another ramp rises from (1, 1) to (4, 7). Find the slope of each ramp and interpret what this means for the difficulty of skating on each ramp.

• The slope of the first ramp is 0, and the slope of the second ramp is 1.

• The slope of the first ramp is 1, and the slope of the second ramp is 2.

• The slope of the first ramp is 3, and the slope of the second ramp is 1.

• The slope of the first ramp is 2, and the slope of the second ramp is 3.

7. A road rises from (0, 0) to (12, 24) while another road rises from (3, 6) to (9, 18). Calculate the slopes of both roads and discuss which road is steeper and how that might affect drivers.

• The slope of the first road is 1, making it steeper.

• Both roads have a slope of 2, indicating they are equally steep.

• Both roads have a slope of 0, meaning they are flat.

• The second road has a slope of 3, indicating it is steeper than the first.

8. A hill has a slope calculated from points (1, 3) to (4, 9) and another hill from (2, 2) to (5, 8). Find the slopes and interpret which hill is steeper and what that means for hikers.

• The second hill has a slope of 1, indicating it is less steep.

• The slopes of both hills are 0, meaning they are flat.

• The first hill has a slope of 3, making it steeper.

• Both hills have a slope of 2, indicating they are equally steep.

9. A ramp for wheelchairs rises from (0, 0) to (8, 4) and another ramp rises from (2, 1) to (6, 5). Calculate the slopes and discuss which ramp is easier to navigate for users.

• Neither ramp is suitable for wheelchair users.

• The second ramp is easier to navigate.

• The first ramp is easier to navigate.

• Both ramps are equally easy to navigate.

10. A mountain trail goes from (0, 0) to (10, 30) and another trail goes from (1, 2) to (9, 26). Determine the slopes of both trails and interpret which trail is steeper and how that might affect hikers' experiences.

• Both trails have a slope of 3, indicating they are equally steep.

• The second trail has a slope of 4, indicating it is less steep.

• The first trail has a slope of 2, making it steeper.

• The first trail has a slope of 3, while the second trail has a slope of 5.